Half-Projected and Projected Hartree-Fock Calculations for Singlet Ground States. i. four-Electron Atomic Systems

The half-projected Hartree-Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF , HPHF and PHF functions are deduced for the ground states of the Li^?, Be, B⁺, and C²⁺ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.     

Ground-state and some excited states of Li2 by the half-projected Hartree–Fock method

The half-projected Hartree–Fock wave function (HPHF ) is one of simplest models for introducing some electronic correlation effects. In this model, the wave function is built up with only two Slater determinants. This simple form suggests its application for the direct determination of singlet excited states. On the other hand, because the HPHF model does not mix singlet and triplet states with M_s = 0, it can be used for determining independently singlet and triplet states without any mutual contamination. In the present work, we applied this model to determine nine electronic states of the lithium molecule; one of them exhibits even the same symmetry of the fundamental one. For this purpose, the 6-311G (d) basis was used. Potential energy curves were determined and some spectroscopic constants derived. The numerical results were compared with the available experimental data, as well as with other theoretical values. © 1995 John Wiley & Sons, Inc.     

MO study of the benzylperoxyl radical, an intermediate in atmospheric ozone formation

Unrestricted Hartree-Fock calculations have been carried out to study the benzylperoxyl radical, an intermediate atmospheric contaminant. For this purpose, quantum mechanical MP2//UHF ab initio calculations were performed by using 6-31G^** and 6-31 + G^** basis sets. Because no previous experimental nor theoretical data were available for benzylperoxyl, the results were compared with those of the smaller unsaturated peroxyl radicals, such as allylperoxyl. It is found that the calculated absolute minimal energy corresponds to a trans conformation in which the O---O bond is sticking away from the benzene ring. Benzylperoxyl is found also to exhibit an unusually O---O small bond order, which reflects the weakness of the bond, i.e. its ability to react with NO forming NO₂ and subsequently ozone. A peculiar MO diagram is obtained, with the unpaired MO deeply located in the “doubly” occupied MO space. This effect is also observed in allylperoxyl. Structural parameters, charges, spin densities and dipole moments are also reported.     

Variational Evaluation of the HSSH FIR Transitions: The Anomalous K-Doubling

The roto-torsional energy levels of HSSH and DSSD up to J = 20 are evaluated variationally with a Hamiltonian expressed in terms of internal coordinates. The kinetic and potential parameters are derived from ab initio calculations with full optimization of the geometry. The calculated levels are employed for the determination of the centrifugal distortion constants. HSSH is a near-prolate symmetric rotor. The most stable C(2) conformer, calculated with MP4(SDQ)/cc-pVQZ, exhibits a 90.55 degrees dihedral angle. For J = 0, the lowest energies of HSSH and DSSD are 413.4876 cm(-1) (n = 1), 798.0304 cm(-1) (n = 2) and 1151.5773 cm(-1) (n = 3), and 304.3185 cm(-1) (n = 1), 594.2919 cm(-1) (n = 2), and 869.3508 cm(-1) (n = 3), respectively. For J = 60, the ab initio calculations allow the reproduction of the anomalous type-K doubling predicted with perturbation theory. Copyright 2000 Academic Press.     

Potential energy surface determinations for nonrigid molecules: Application to acetone

In the present work, the problem of the determination of the potential energy surface for nonrigid molecules is examined in the case of the double rotation of the methyl groups in acetone. From the symmetry adapted functional form for the potential, the minimum number of configurations to be calculated is deduced in order to have a reliable surface. With this consideration in mind, the potential energy surface of acetone is determined in some Hartree–Fock semiempirical (CNDO /2) and ab initio procedures with different standard basis sets. In addition, ab initio calculations are performed using different sets of floating Gaussian functions in order to introduce some polarization effects in the wave function. Finally, the influence of the electronic correlation effects in the barrier height, and the role of the possible relaxation of the structure during the rotation is discussed.     

The non-rigid group for wagging and torsion modes in methvlamine

The non-rigid group (NRG) for the wagging and torsion motions in methylamine is deduced in terms of rotation and inversion operations. The group is compared to that of LonguetHiggins for the same molecule expressed in terms of permutations and permutations-inversion. It is seen that the NRG is isomorphic to that of Longuet-Higgins and the C_{6 v} symmetry point group. The character table is deduced, as well as the symmetry eigenvectors in terms of products of trigonometric functions. Selection rules for the infrared torsional-wagging transitions are given, and the band profiles of the spectrum discussed.     

Exploring potential energy hypersurfaces for triple symmetric inversion in 3-azabicyclo[3.3.1]nonan-9-one and its N-methyl derivative

The potential energy hypersurfaces for the triple inversion, from chair to boat and α to β conformations, are explored theoretically in 3-azabicyclo[3.3.1]nonan-9-one and its N-methyl derivative, by using ab initio quantum-mechanical calculations. Both compounds are precursors of rigid analogs of the potential GABA_A and GABA_B receptor antagonists. In contrast to results from semiempirical calculations, the chair–chair β conformers are found to be, by far, the most stable structures for both the nonmethylated and N-methylated compounds. The inversion barriers are found to be relatively low, so that the conformers could be expected to exist in thermodynamic equilibrium at room temperature. A population analysis reveals, however, that, in the ab initio approach, the molecules seem to exist practically only in the chair–chair–β conformation. The theoretical results compare well with the available experimental data. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1567–1574, 1998     

Cndo/2 conformational calculation for conjugated and non-conjugated molecular systems

In order to check the effectiveness of the well known CNDO/2 method for predicting molecular conformations, twenty-six molecular systems, involving B, C, N, O, F, Si, S and Cl atoms, were studied. If these molecules are classified into three groups, according to simple rules, the CNDO/2 method is found to fail systematically in one of them. In this group the twisted bond is expected to be delocalized. It is concluded that the CNDO/2 method is not useful in predicting conformations of molecules in which the twisted bond is delocalized.     

The interlaboratory comparison "IMEP-19 trace elements in rice"—a new approach for measurement performance evaluation

The aim of IMEP is to present objectively the quality of chemical measurements. Participants in IMEP compare their reported measurement results with independent external certified reference values with demonstrated traceability and uncertainty, as evaluated according to international guidelines. IMEP-19 focused on measurements of trace elements in rice aiming to support the Commission Regulation (EC) No. 466/2001 on maximum levels for certain contaminants in foodstuff. Measurement results for the elements Cd, Cu, Pb and Zn were reported by 267 field laboratories involved in food analysis from 43 countries. Performance criteria for the evaluation of the reported measurement results in IMEP-19 are suggested. The chosen performance indicators not only take into account the deviation of the reported measurement value from the certified reference value, but also set criteria for maximum and minimum acceptable uncertainty. The IMEP-19 participants' performance is reviewed by means of using new simple graphical tools, called "Naji plots".     

Internal dynamics of nonrigid molecules. I. Application to acetone

The group theory for nonrigid molecules is used for studying the internal dynamics of the two equivalent C_3v rotor “bent” molecules. Special emphasis is given to the deduction of the symmetry basis vectors which represent in box form the Hamiltonian operator. It is shown that these basis vectors may be advantageously employed in order to simplify the resolution of the two-rotor equation. The procedure is applied to the acetone molecule. It is found that the lowest solutions are clustered into groups of four. The four lowest levels are related to vibrational states, the upper 64 to vibro–rotational states, in which the rotors are rotating in a restricted manner. Only few states show some cogwheel effect. Internal rotation contributions to the principal thermodynamic parameters of acetone are also computed.